






"""simple docstring"""





from numpy import exp, pi, sqrt







def 	lowerCamelCase__			(				_lowerCamelCase			:						List[Any]						,							_lowerCamelCase			:						float = 0.0						,							_lowerCamelCase			:						float = 1.0					) ->							int:
  return 1 / sqrt(2 * pi * sigma**2					) * exp(-((x - mu) ** 2) / (2 * sigma**2)					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()












"""simple docstring"""





_SCREAMING_SNAKE_CASE   :							Optional[int]          =		8.314_4598







def 	lowerCamelCase__			(				_lowerCamelCase			:						float						,							_lowerCamelCase			:						float					) ->							float:
  if temperature < 0:
    raise Exception('Temperature cannot be less than 0 K'					)
  if molar_mass <= 0:
    raise Exception('Molar mass cannot be less than or equal to 0 kg/mol'					)
  else:
    return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
  import doctest

  # run doctest
  doctest.testmod()

  # example
  _SCREAMING_SNAKE_CASE   :							List[Any]          =		300
  _SCREAMING_SNAKE_CASE   :							Dict          =		28
  _SCREAMING_SNAKE_CASE   :							List[str]          =		rms_speed_of_molecule(temperature, molar_mass)
  print(F'''Vrms of Nitrogen gas at 300 K is {vrms} m/s''')




